I've setup my Xbox One controller with Dolphin and it's working brilliantly - both triggers are mapped to L, R, L-analog and R-analog, so I get full analogue triggers. They cannot be used at the same time though - when I hold one, then hold the other, it cancels out the first one.

A few suggestions on here said to use XINPUT rather than DINPUT, but I am using XINPUT. The L and R triggers are both seen as the same axis: Z- and Z+, which is where I'm thinking the problem lies.

Is there any way of fixing this?

The emulator is stunning, by the way. Runs perfectly on my system, looks and sounds just like it does on the real console.

Ahh! Totally my mistake. It was listed as 'XINPUT compatible device', but was actually using dinput. After disabling and re-enabling the controller I managed to get xinput to show up separately. Thanks!